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3 years ago

The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?

Mathematics

2 answers:

timofeeve [1]3 years ago

5 0

Answer:

g is decreasing for all x less than or equal to -1

Step-by-step explanation:

The graph of the function y = |x| looks like a "vee."

g(x) = |x + 1| - 7 moves that graph 1 unit to the left (I know, it looks backwards!) and down 7 units. See attached image.

Function g(x) is decreasing for all $x \le -1$ .

mihalych1998 [28]3 years ago

4 0

Answer:

on edg3

Step-by-step explanation:

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Suppose that the function g is defined, for all real numbers, as follows.

svetoff [14.1K]

Answer:

a) g(-2) = 0

b) g(-1) =1

c) g(4) = 2

Step-by-step explanation:

Given data

$g(x) = \frac{-1}{4x+1} if x < -2$

$g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2$

$g(x) = 2 if x >2$

Step( i ):-

$g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2$

put x = -2

$g(-2) = -(-2+1)^{2} +1 = -(-1)^{2}+1 = -1+1 =0$

g(-2) = 0

Step(ii):-

$g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2$

Put x = -1

$g(-1) = -(-1+1)^{2} +1 = -(0)^{2}+1 = -0+1 =1$

g(-1) =1

Step(iii):-

$g(x) = 2 if x >2$

g(4) = 2

7 0

3 years ago

Paul has 12 coins in his pocket, consisting entirely of dimes and quarters. If he has a total of 195 cents in coins, how many co

anyanavicka [17]

Let x be the number of dimes

and y be the number of quarters

Total number of coins = 12

So number of dimes + number of quarters = total number of coins

x + y = 12 ---------> equation 1

We know, 1 Quarter = 25 cents, 1 Dime = 10 cents, total cents = 196

y quarters = 25y cents , x dimes = 10x cents

x dimes + y quarters = 195 cents

10x + 25y = 195 -----------> equation 2

Now solve both equations

x + y =12, we solve for y by subtracting x on both sides

y = 12-x

Now substitute y in second equation

10x + 25(12-x) = 195

10x + 300 -25x = 195 (combine like terms)

-15x + 300 = 195 (subtract 300 on both sides)

-15x = -105 ( divide by -15)

x=7

y= 12-x

y=12-7 = 5

The number of dimes = 7

Number of quarters = 5

8 0

3 years ago

What is the point-slope form of a line with slope -5 that contains the point a (2,-1)?

gulaghasi [49]

The point-slope form the line which has the value of slope -5 and contains a point as A(2,-1) is (y+1)=-5(x-2).

<h3>What is point slope form?</h3>

The point slope form of a line is the expression of line which has a specified slope and passes through a point.

The point slope form is givne as,

(y-y₁)=m(x-x₁)

Here, m is the slope of the line, x₁ is the x coordinate of the point by which line passes and y₁ is the y coordinate of the same point.

The slope of a line is -5. This line contains the point A (2,-1). Thus, the point slope form is,

(y-y₁)=m(x-x₁)

(y-(-1))=-5(x-2)

(y+1)=-5(x-2)

Thus, the point-slope form the line which has the value of slope -5 and contains a point as A(2,-1) is (y+1)=-5(x-2).

Learn more about the point slope form here;

brainly.com/question/6497976

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2 years ago

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adoni [48]

Answer:

so it is a rectangle with a perimeter of 30 units

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Brums [2.3K]

Answer:

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